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Semi-SupervisedClassificationBasedonGraphFiltering JieFan,CihanTepedelenlioglu,AndreasSpanias

SenSIPCenter,SchoolofECEE,ArizonaStateUniversity

MOTIVATION

q Graphscancapturecomplexrelationalcharacteristics.q Signalprocessingongraphsextendstheclassicaldiscretesignalprocessingtheorytosignalsindexedbyverticesofagraph.

GRAPHFILTERDIAGRAM

MONTECARLOSIMULATIONRESULTS

SensorSignalandInformationProcessingCenterhttp://sensip.asu.edu

•  [1]S.Chen,A.Sandryhaila,J.M.MouraandJ.Kovacevic,“Adaptivegraphfiltering:Multiresolutionclassificationongraphs,”IEEEGlobalSIP,2013,pp.427–430.

•  [2]S.Chen,F.Cerda,P.Rizzo,J.Bielak,J.H.Garrett,andJ.Kovacevic,“Semi-supervisedmultiresolutionclassificationusingadaptivegraphfilteringwithapplicationtoindirectbridgestructuralhealthmonitoring,”IEEETrans.onSignalProcessing,vol.62,pp.2879–2893,2014.

•  [3]G.Caldarelli,A.Chessa,F.Pammolli,A.Gabrielli,andM.Puliga,“Reconstructingacreditnetwork,”NaturePhysics,vol.9,no.3,pp.125–126,2013.

ThisworkisfundedinpartbytheNSFawardECSS1307982,NSFCPSaward1646542andtheSenSIPCenter.

POTENTIALAPPLICATIONS

q  Awelldesignedgraphfilterworksasasemi-supervisedclassifier.q Theproposed filterdesigningmethodprovides lowererror rate than the

conventionalonewhenfeaturedataisincomplete.q  Ourmethodisespeciallysuitableforpracticalapplicationthatthe initial

information is insufficient or quite correct due to privacy policies andmeasuringdifficulties.

q Aclassifierfordatalabeling.q Anerrordetectorfornetworkanalysis.q Asimplerepresentationforimagesincomputervision.q Apre-processofneuralnetworksforreducingcomputationandmitigatingoverfittingrisk.

PROBLEMSTATEMENT

GRAPHFILTERINGPROCEDURE

q Apartiallylabeleddatasetwithgraphencodedinnerinteraction.Graphvertices:datapoints.Graphedges:relationshipsamongthevertices.

q Agraphshiftmatrixisgeneratedfromthedataset.q Thefeaturesofverticesisnotcompletelycollected.q Eigenvaluesandeigenvectorsneedtobeupdated.

ACKNOWLEDGEMENTS

REFERENCES

CONCLUSIONq GraphFiltering:

q ConventionalGraphFilterDesignMethod:

q ProposedGraphFilterDesignMethod:

Y = H ⋅ X = QΛQ−1( ) ⋅ X

H =Q h0 + h1Λ + h2Λ2 +!+ hLΛ

L( )Q−1

Hk+1 = Hk !Rk

Ai , j =exp − Xi − X j 2

σ( )exp − Xi − X j 2

σ( )i∑

Rk = f X ,Hk( )